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    "# Sequential Domain Reduction\n",
    "\n",
    "## Background\n",
    "Sequential domain reduction is a process where the bounds of the optimization problem are mutated (typically contracted) to reduce the time required to converge to an optimal value. The advantage of this method is typically seen when a cost function is particularly expensive to calculate, or if the optimization routine oscilates heavily. \n",
    "\n",
    "## Basics\n",
    "\n",
    "The basic steps are a *pan* and a *zoom*. These two steps are applied at one time, therefore updating the problem search space evey iteration.\n",
    "\n",
    "**Pan**: recentering the region of interest around the most optimal point found.\n",
    "\n",
    "**Zoom**: contract the region of interest.\n",
    "\n",
    "![](sdr.png)\n",
    "\n",
    "\n",
    "## Parameters\n",
    "\n",
    "There are three parameters for the built-in `SequentialDomainReductionTransformer` object:\n",
    "\n",
    "\n",
    "$\\gamma_{osc}:$ shrinkage  parameter  for  oscillation. Typically [0.5-0.7]. Default = 0.7\n",
    "\n",
    "$\\gamma_{pan}:$ panning parameter. Typically 1.0. Default = 1.0\n",
    "\n",
    "$\\eta:$ zoom parameter. Default = 0.9\n",
    "\n",
    "\n",
    "More information can be found in this reference document:\n",
    "\n",
    "---\n",
    "\n",
    "Title: \"On the robustness of a simple domain reduction scheme for simulation‐based optimization\" \n",
    "\n",
    "Date: 2002 \n",
    "\n",
    "Author: Stander, N. and Craig, K. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---\n",
    "Let's start by importing the packages we'll be needing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from bayes_opt import BayesianOptimization\n",
    "from bayes_opt import SequentialDomainReductionTransformer\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's create an example cost function. This is the [Ackley function](https://en.wikipedia.org/wiki/Ackley_function), which is quite non-linear. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ackley(**kwargs):\n",
    "    x = np.fromiter(kwargs.values(), dtype=float)\n",
    "    arg1 = -0.2 * np.sqrt(0.5 * (x[0] ** 2 + x[1] ** 2))\n",
    "    arg2 = 0.5 * (np.cos(2. * np.pi * x[0]) + np.cos(2. * np.pi * x[1]))\n",
    "    return -1.0 * (-20. * np.exp(arg1) - np.exp(arg2) + 20. + np.e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the standard bounds for this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "pbounds = {'x': (-5, 5), 'y': (-5, 5)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "This is where we define our `bound_transformer` , the Sequential Domain Reduction Transformer\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "bounds_transformer = SequentialDomainReductionTransformer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can set up two idential optimization problems, except one has the `bound_transformer` variable set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mutating_optimizer = BayesianOptimization(\n",
    "    f=ackley,\n",
    "    pbounds=pbounds,\n",
    "    verbose=0,\n",
    "    random_state=1,\n",
    "    bounds_transformer=bounds_transformer\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mutating_optimizer.maximize(\n",
    "    init_points=2,\n",
    "    n_iter=50,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "standard_optimizer = BayesianOptimization(\n",
    "    f=ackley,\n",
    "    pbounds=pbounds,\n",
    "    verbose=0,\n",
    "    random_state=1,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "standard_optimizer.maximize(\n",
    "    init_points=2,\n",
    "    n_iter=50,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After both have completed we can plot to see how the objectives performed. It's quite obvious to see that the Sequential Domain Reduction technique contracted onto the optimal point relativly quickly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(mutating_optimizer.space.target, label='Mutated Optimizer')\n",
    "plt.plot(standard_optimizer.space.target, label='Standard Optimizer')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the actual contraction of one of the variables (`x`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# example x-bound shrinking\n",
    "x_min_bound = [b[0][0] for b in bounds_transformer.bounds]\n",
    "x_max_bound = [b[0][1] for b in bounds_transformer.bounds]\n",
    "x = [x[0] for x in mutating_optimizer.space.params]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0x7fc7471db5e0>"
     },
     "metadata": {},
     "execution_count": 12
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(x_min_bound[1:], label='x lower bound')\n",
    "plt.plot(x_max_bound[1:], label='x upper bound')\n",
    "plt.plot(x[1:], label='x')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
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